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On extremum-searching approximate probabilistic algorithms. (English) Zbl 0543.03029

The author proposes a simple probabilistic algorithm (similar to that of the Monte Carlo method) for an approximation of the maximum value of a recursive function defined on a finite set. It is shown, too, that if this function is regular or continuous in a sense, then its maximum value can be relatively approximated with a computational complexity which is substantially smaller than that of corresponding deterministic procedures.
Reviewer: V.Ja’kl

MSC:

03D20 Recursive functions and relations, subrecursive hierarchies
03D15 Complexity of computation (including implicit computational complexity)
41A99 Approximations and expansions
65D99 Numerical approximation and computational geometry (primarily algorithms)
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References:

[1] A. V. Aho J. E. Hopcroft, J. D. Ullman: The Design and Analysis of Computer Algorithms. Reading, Addison-Wesley, London 1974 · Zbl 0326.68005
[2] M. O. Rabin: Probabilistic algorithms. Proceedings of the Symposium 1976, Carnegie-Mellon Univ., Pittsburgh, Academic Press, New York 1976, pp. 21 - 39. · Zbl 0384.60001
[3] I. Kramosil: Statistical verification procedures for propositional calculus. Computers and Artificial Intelligence 2 (1983), 3, 235-258. · Zbl 0529.68066
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